论文标题
在谎言和量子代数方面，对Askey-Wilson类型代数的新实现
New realizations of algebras of the Askey-Wilson type in terms of Lie and quantum algebras
论文作者
论文摘要
ASKEY-WILSON代数是根据量子代数$ u_q（\ Mathfrak {su}（2））$或$ u_q（\ Mathfrak {su}（su}（1,1））$的元素实现的。还给出了RACAH代数的新实现。提供了不同专业的详细信息。这些新实现的优点是，Askey-Wilson（或Racah）代数的一个发生器在量子代数的通常表示中变成对角线，而第二个代数为Tridiagonal。这允许轻松恢复ASKEY方案相关的正交多项式的复发关系。这些实现涉及量子代数的cartan发电机的合理函数，它们相对于其他发电机是线性的，并且取决于量子代数的Casimir元素。
The Askey-Wilson algebra is realized in terms of the elements of the quantum algebras $U_q(\mathfrak{su}(2))$ or $U_q(\mathfrak{su}(1,1))$. A new realization of the Racah algebra in terms of the Lie algebras $\mathfrak{su}(2)$ or $\mathfrak{su}(1,1)$ is given also. Details for different specializations are provided. The advantage of these new realizations is that one generator of the Askey-Wilson (or Racah) algebra becomes diagonal in the usual representation of the quantum algebras whereas the second one is tridiagonal. This allows to recover easily the recurrence relations of the associated orthogonal polynomials of the Askey scheme. These realizations involve rational functions of the Cartan generator of the quantum algebras, they are linear with respect to the other generators and depend on the Casimir element of the quantum algebras.
